During the debate, Trump bragged about the size of his penis and dismissed Rubio as "Little Marco" and Cruz as "Lying Ted." Cruz mocked Trump, telling him to "breathe." And Rubio called Trump a "con artist."

Priebus has sought to maintain control of his party, even as it appears to be splintering apart.

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He was pressed on the "autopsy" that the RNC compiled after 2012's losses, underscoring that the party needs to reach out to Latinos and emphasize respect.

Priebus said he agrees "with every word" from the report.

"And I think it's really important," he said. "I think dignity and respect is something that should be at the center of everything that we do."

Priebus said he "highly" doubts that GOP voters won't have awarded one candidate the 1,237 delegates it takes to capture the nomination before the Republican National Convention.

If the contest isn't closer to settled in early April, though, the prospect of a contested convention merits more attention, he said.

"I just don't see that happening," he said. It doesn't mean it's impossible, it just means that you don't know what next week is going to bring, or the week after, or a month from now. I would say that if we have an interview in a month and it's still some sort of tied scenario, then I think people start talking about it more clearly.

"But I just think these are hypotheticals at this point, there's a long way to go."